Parsimonious Shifted Asymmetric Laplace Mixtures
This work provides an incremental improvement for statistical modeling in clustering and classification by adapting an existing framework to a non-Gaussian distribution.
The authors introduced a family of parsimonious shifted asymmetric Laplace mixture models by extending the mixture of factor analyzers to this distribution, with constraints on component scale matrices to create parsimonious variants. They applied these models to real data, comparing them to Gaussian analogues in clustering and classification tasks.
A family of parsimonious shifted asymmetric Laplace mixture models is introduced. We extend the mixture of factor analyzers model to the shifted asymmetric Laplace distribution. Imposing constraints on the constitute parts of the resulting decomposed component scale matrices leads to a family of parsimonious models. An explicit two-stage parameter estimation procedure is described, and the Bayesian information criterion and the integrated completed likelihood are compared for model selection. This novel family of models is applied to real data, where it is compared to its Gaussian analogue within clustering and classification paradigms.